Problem: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$8.50$, and bags of cookies cost $$4.50$, and sales equaled $$61.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Explanation: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8.5x+4.5y = 61}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${8.5x + 4.5}{(x+2)}{= 61}$ Simplify and solve for $x$ $ 8.5x+4.5x + 9 = 61 $ $ 13x+9 = 61 $ $ 13x = 52 $ $ x = \dfrac{52}{13} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(4)}{ + 2}$ ${y = 6}$ You can also plug ${x = 4}$ into $ {8.5x+4.5y = 61}$ and get the same answer for $y$ ${8.5}{(4)}{ + 4.5y = 61}$ ${y = 6}$ $4$ bags of candy and $6$ bags of cookies were sold.